In article <3j0i8g$
...@netnews.upenn.edu>,
h
...@saul.cis.upenn.edu (Hong-liang Xie) writes:
|> Can anybody point me to references on first-order
|> logic with partial functions? It's much appreciated.
|>
Below you find some references in BiBTeX format.
A range of approaches to deal with partial functions are
reviewed in [CJ91] and [MR91]. A recent and comprehensive
description of LPF (Logic of Partial Functions) is given
in [JM94]. The oldest reference is probably [Kle52].
Best regards,
Kees Middelburg
P.S. [MR91] and [JM94] are available in PostScript format
by FTP: ftp://ftp.phil.ruu.nl/pub/logic/keesm/
by WWW: http://www.phil.ruu.nl/home/keesm/
@article{Avr91,
author = "A. Avron",
title = "Natural 3-valued Logics {--} Characterization and Proof Theory",
journal = "Journal of Symbolic Logic",
volume = 56, year = 1991, pages = "276--294"}
@article{BCJ84,
author = "H. Barringer and J.H. Cheng and C.B. Jones",
title = "A Logic Covering Undefinedness in Program Proofs",
journal = "Acta Informatica",
volume = 21, year = 1984, pages = "251--269"}
@book{Bee85,
author = "M.J. Beeson",
title = "Foundations of Constructive Mathematics",
publisher = "Springer Verlag",
year = 1985}
@article{Bee88,
author = "M.J. Beeson",
title = "Towards a Computation System Based on Set Theory",
journal = "Theoretical Computer Science",
volume = 60, year = 1988, pages = "297--340"}
@incollection{Bla86,
author = "S. Blamey",
title = "Partial Logic",
booktitle = "Handbook of Philosophical Logic, Volume~III",
editor = "D. Gabbay and F. Guenther",
publisher = "D. Reidel Publishing Company",
year = 1986, chapter = "III.1"}
@phdthesis{Che86,
author = "J.H. Cheng",
title = "A Logic for Partial Functions",
school = "University of Manchester, Department of Computer Science",
note = "Technical Report UMCS-86-7-1",
year = 1986}
@inproceedings{CJ91,
author = "J.H. Cheng and C.B. Jones",
title = "On the Usability of Logics which handle Partial Functions",
booktitle = "3rd Refinement Workshop",
editor = "C. Morgan and J.C.P. Woodcock",
publisher = "Springer Verlag, Workshops in Computing Series",
year = 1991, pages = "51--69"}
@article{GL90,
author = "A. {Gavilanes-Franco} and F. {Lucio-Carrasco}",
title = "A First Order Logic for Partial Functions",
journal = "Theoretical Computer Science",
volume = 74, year = 1990, pages = "37--69"}
@book{GMW79,
author = "M.J.C. Gordon and R. Milner and C. Wadsworth",
title = "Edinburgh LCF",
publisher = "Springer Verlag, LNCS~78",
year = 1979}
@article{Hol91,
author = "M. Holden",
title = "Weak Logic Theory",
journal = "Theoretical Computer Science",
volume = 79, year = 1991, pages = "295--321"}
@article{Hoo87,
author = "A. Hoogewijs",
title = "Partial-Predicate Logic in Computer Science",
journal = "Acta Informatica",
volume = 24, year = 1987, pages = "381--393"}
@article{JM94,
author = "C.B. Jones and C.A. Middelburg",
title = "A Typed Logic of Partial Functions Reconstructed Classically",
journal = "Acta Informatica",
volume = 31, year = 1994, pages = "399--430"}
@book{Kle52,
author = "S.C. Kleene",
title = "Introduction to Metamathematics",
publisher = "North-Holland",
year = 1952}
@inproceedings{KTB88,
author = "B. Konikowska and A. Tarlecki and A. Blikle",
title = "A Three-valued Logic for Software Specification and Validation",
booktitle = "VDM~'88",
editor = "R. Bloomfield and L. Marshall and R. Jones",
publisher = "Springer Verlag, LNCS~328",
year = 1988, pages = "218--242"}
@inproceedings{KR89,
author = "C.P.J. Koymans and {Renardel de Lavalette}, G.R.",
title = "The Logic {$\mbox{MPL}\sb\omega$}",
booktitle = "Algebraic Methods: Theory, Tools and Applications",
editor = "M. Wirsing and J.A. Bergstra",
publisher = "Springer Verlag, LNCS~394",
year = 1989, pages = "247--282"}
@incollection{Luk67,
author = "J. {\L}ukasiewicz",
title = "On Three-valued Logic",
booktitle = "Polish Logic 1920--1939",
editor = "S. McCall",
publisher = "Oxford University Press",
year = 1967}
@incollection{McC67,
author = "J. McCarthy",
title = "A Basis for a Mathematical Theory of Computation",
booktitle = "Computer Programming and Formal Systems",
editor = "P. Braffort and D. Hirschberg",
publisher = "North-Holland Publishing Company",
year = 1967, pages = "33--70"}
@inproceedings{MR91,
author = "C.A. Middelburg and {Renardel de Lavalette}, G.R.",
title = "{LPF} and {$\mbox{MPL}\sb\omega$} {--}
A Logical Comparison of {VDM SL} and {COLD-K}",
booktitle = "VDM~'91, Volume~1",
editor = "S. Prehn and W.J. Toetenel",
publisher = "Springer Verlag, LNCS~551",
year = 1991, pages = "279--308"}
@book{Pau87,
author = "L.C. Paulson",
title = "Logic and Computation",
publisher = "Cambridge University Press,
Cambridge Tracts in Theoretical Computer Science 2",
year = 1987}
@unpublished{Plo85,
author = "G.D. Plotkin",
title = "Partial Function Logic",
note = "Lectures at Edinburgh University",
year = 1985}
@article{Ren84,
author = "{Renardel de Lavalette}, G.R.",
title = "Descriptions in Mathematical Logic",
journal = "Studia Logica",
volume = 43, year = 1984, pages = "281--294"}
@inproceedings{Sco67,
author = "D.S. Scott",
title = "Existence and Description in Formal Logic",
booktitle = "Bertrand Russell, Philosopher of the Century",
editor = "R. Schoenman",
publisher = "Allen {\&} Unwin",
year = 1967, pages = "181--200"}
@inproceedings{Sco79,
author = "D.S. Scott",
title = "Identity and Existence in Intuitionistic Logic",
booktitle = "Applications of Sheaves",
editor = "M.P. Fourman and C.J. Mulvey and D.S. Scott",
publisher = "Springer Verlag, Lecture Notes in Mathematics~753",
year = 1979, pages = "660--696"}
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